One goal of circuit design and/or program coding is to optimize some aspect of a system with the goal of improving its quality. One such optimization approach, generally referred to as the retiming of a circuit, is a technique of moving the structural location of latches or registers in a digital circuit in order to improve performance, area, and/or power consumption in such a way that preserves behavior at the circuit's outputs. Automated techniques use a directed graph to represent the digital circuit under consideration, where the vertices of the graph represent asynchronous combinational blocks, and directed edges of the graph represent a series of synchronous registers or latches. Each vertex has a value corresponding to the delay through the combinatorial circuit. After constructing this representation, one can attempt to optimize the circuit by moving delay registers around from input to the output or vice versa.